关于树的补图的色多项式

On chromatic polynomials of complement graph of trees

本文证明了,由树的特征多项式可立即求出其补图的色多项式.

The following theorem is Proved:Theorem If G is a tree,Let characteristic polynomial of G be P (G,λ)=λ~n-c_2λ^(n-2)+c_4λ(n-4)-c_6λ(n-6)+……Let Chromatic polynomial of ■ be f(■,t)=[t]_n+b_1[t]_n+b_2[t]_(n-2)+…+b_(6-1)[t-]_1where [t]_k-t(t-1)(t-2)…(t-k+1),(k=1,2,…,n) then b-i=c_(2i).(i=1,2, 3,…).